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Gaiane Panina

Gaiane Panina is a professor at the St. Petersburg Institute for Informatics and Automation of the Russian Academy of Science. Her research interests are convex polytopes, Combinatorial Geometry, polygonal linkages, with illustrations here. She particularly enjoys participation in mathematical schools, both lecturing and attending classes given by her colleagues.

 Gaiane Panina

 

"Configuration Spaces":

  • What (topologically) is the set of unordered pairs of points lying on the circle S^1?
  • Take four bars and join them consecutively by revolving joints in a closed flexible chain.

What is the set of all possible 3D shapes of the chain? These are relatively simple questions about configuration spaces. More detailed, we have the following paradigm: here is some combinatorial (or combinatorial plus metrical) object A. It can be just everything: a configuration of points with prescribed collinearities, a graph with prescribed edge lengths, a face lattice of a polytope, etc. The object A can be geometrically realized in many ways. The set of all realizations is by definition the configuration space of A. To describe the configuration space is always a kind of art. The aim of my lecture is to present a diversity of methods used in this subject.